Physics

Problem

A commuter car travels along a straight east–west track. Let the positive direction be east. The motion is described chronologically as follows. 1. From

t=0\,\text{s}

t=5\,\text{s}

the car moves east at a constant speed of

15\,\text{m/s}

. 2. Starting at

t=5\,\text{s}

the car experiences a constant westward acceleration of

3.0\,\text{m/s}^{2}

until it comes to rest at a traffic light. 3. The car remains at rest for

3.0\,\text{s}

while waiting for the light. 4. Immediately after the wait the car accelerates westward at

2.0\,\text{m/s}^{2}

for

4.0\,\text{s}

. 5. Finally, the driver applies the brakes, bringing the car to rest in

1.0\,\text{s}

with constant acceleration. Ignore all effects of friction and air resistance. (a) On axes in your response booklet, sketch a velocity–time graph for the entire motion described above, covering the time interval from

t=0\,\text{s}

until the car stops in step 5. Label the numerical value of the velocity at the start of each interval, the instants when the velocity is zero, and the duration of each interval. (b) Using the graph from part (a), sketch a qualitative position–time graph for the same time interval. Clearly indicate the location of the traffic light, the maximum eastward position, and the final stopping point. (c) Determine the car’s total displacement relative to its starting position for the entire trip. Show your reasoning. (d) Identify every time interval during which the car’s speed is increasing while its acceleration is westward. Explain how your velocity–time graph supports your answer.

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